MECHANICAL ANALYSIS OF DINOSAUR EGGSHELLS AND SHEDS NEW LIGHT ON THE CONTACT-INCUBATION BEHAVIOR IN DINOSAURS

1. Mechanical Analysis of Dinosaur Eggshells Sheds New Light
on the Contact-incubation Behavior in Dinosaurs
Hsiao-Jou Wu1,2, Hon-Tsen Yu1, Tzu-Ruei Yang3* , and Jia-Yang Juang2*
1Department of Life Science, National Taiwan University, Taipei, Taiwan
2Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
3Division of Geology, National Museum of Natural Science, Taichung, Taiwan
*E-mail of the corresponding author
tzurueiyang@nmns.edu.tw
jiayang@ntu.edu.tw
1

2. 2
b
10 cm
Since the adult-associated clutches were discovered (Fig. 1) (Norell et al., 1995), the debate of dinosaurs’ contact-incubation has lasted for a long time.
However, the ratio of egg mass and adult mass in dinosaurs (0.59% for Citipati osmolskae) is much lower than extant birds (approximately 5%).
Additionally, there are diversified shapes and sizes within dinosaur eggs (Fig. 2). We wonder whether the dinosaur egg could bear a load of their
parents by contact-incubation, first of all, we have to quantify the stiffness of dinosaur eggs.
Introduction
IGM 100/1004
(Norell et al. 2018)
10 cm
Citipati osmolskae
IGM 100/979
(Norell et al., 1995)
Fig. 2. A simplified phylogeny of Dinosauria includes the dinosaur clades
analyzed in this study. The egg models on the right column represent the egg
shapes from those dinosaur groups.
Fig. 1. The specimens of
adult-associated clutches
of Citipati osmolskae

3. 3
In our previous research, we found that the C number was almost constant among 400 extant avian species (Juang et al.,
2017). C number is dimensionless and represents an egg’s relative stiffness with respect to its weight (Fig. 3A). Our finite
element analysis using ANSYS allows us to simulate the stiffness of dinosaur eggs based on fossil remains (Fig. 3B). Our
result shows that the eggs of Oviraptoridae and Caenagnathidae are more fragile than those of extant avians due to
their lower C number (Fig. 3C).
Dimensionless number (C number)
𝐶 =
𝐴2
𝐾
𝐵𝑊
𝐾 =
𝐹
𝛿
(Juang et al., 2017)
0.083
C W 

Fig. 3 (A) Parameters of C number. (B) The egg model created by ANSYS APDL. (C) C number of dinosaur eggs compared with extant avian and extinct
ratites. The gray line is the regression from Aves. Colors indicate dinosaur groups.
A B C
A Width
B Length
K Stiffness
W Egg weight
F Force
𝜹 Displacement

4. 4
𝐹. 𝑆. =
𝐶
𝐶𝑐𝑟
Clutch Model Simulation
The Factor of Safety (F.S.) is to quantify the load-bearing capacity of an egg. The 𝐶𝑐𝑟 of F.S. is calculated from critical thickness which is the thinnest
thickness of eggshell loaded by parent’s body mass. To simulate how the eggs deform under the contact-incubation scenario, we built the whole
clutch and imitated the situation buried in the soil (Fig. 4). We focused on the exquisitely preserved adult-associated clutches of troodontid and
oviraptorosaurian. (as shown in Figure 5-7).
Fig. 5-7. Clutch specimens and models. Scale bar: 10 cm (A) Adult-associated
clutch specimen (B) Top view of clutch model. The circle of dash line represents
the range covered by parents.
Fig. 5 (C) Oblique view of the same model shows eggs incline at 70° (possible
slope inclination 70° to 90° (Zhao & Ma (1997)).
Fig. 6-7 (C) Oblique view of the same model shows eggs incline at 35° (possible
slope inclination 35° to 40° (Yang et al., 2019)).
Fig. 4. Side view of clutch model of Troodon formosus. The red arrow
represents the force equal to body mass. The range with orange color at the
bottom represents the boundary condition which is fixed all degrees of
freedom. The magnified position shows the area with a flat state. (Norell et al., 2018)
IGM 100/1004
Troodon formosus
Citipati osmolskae
Heyuannia huangi
NMNS004529-F003855
(Varricchio et al. 1997)
MOR963

5. 5
References
Juang, J. Y., Chen, P. Y., Yang, D. C., Wu, S. P., Yen, A., et al. (2017). The avian egg exhibits general allometric invariances in mechanical design. Scientific Reports, 7, 14205.
Norell, M. A., Balanoff, A. M., Barta, D. E., & Erickson, G. M. (2018). A second specimen of Citipati Osmolskae associated with a nest of eggs from Ukhaa Tolgod, Omnogov Aimag, Mongolia. American Museum Novitates, 3899, 1-44.
Norell, M. A., Clark, J. M., Chiappe, L. M., & Dashzeveg, D. (1995). A nesting dinosaur. Nature, 378, 774-776.
Varricchio, D. J., Jackson, F. D., Borkowski, J. J., & Horner, J. R. (1997). Nest and egg clutches of the dinosaur Troodon formosus and the evolution of avian reproductive traits. Nature, 385.
Varricchio, D. J., et al. (2002). Embryos and eggs for the Cretaceous theropod dinosaur Troodon formosus. Journal of Vertebrate Paleontology, 22, 564-576.
Yang, T.-R., Wiemann, J., Xu, L., Cheng, Y.-N., Wu, X.-C., et al. (2019). Reconstruction of oviraptorid clutches illuminates their unique nesting biology. Acta Palaeontologica Polonica, 64(3).
Zhao, Z., & Ma, H. (1997). Biomechanical properties of dinosaur eggshells (Ⅵ)── the stability of dinosaur eggshell under external pressure. Vertebrata PalAsiatica, 88-101.
Acknowledgement
Thanks to the three advisors, Dr. Hon-Tsen Yu for part of biology, Dr. Jia-Yang Juang for part of
mechanical engineering and simulation, Dr. Tzu-Ruei Yang for part of dinosaurs and making
connections with museums. Thanks also to members of three labs. And we thank National Museum
of Natural Sciences and Shishang Museum of Natural History for providing fossil egg specimens.
Fig. 8. (A) Restoration of
incubation behavior of
Troodontidae, in which eggs
were semi-buried. (B)
Restoration of incubation
behavior of Oviraptoridae,
which was a center devoid of
eggs. (C) Factor of Safety of
the dinosaur clutches
compared with Aves. The
red dash line represents F.S.
equal to 2, which is the
lowest boundary of Aves.
Shapes indicate slope angles.
(Varricchio et al. 2016)
(Varricchio et al. 2016)
Conclusions
1. We could use the method of C number to normalize
the stiffness of dinosaur eggs.
2. C number of Oviraptoridae and Caenagnathidae eggs
are lower than those of avians, indicating that they are
more fragile than extant avian eggs and might not be
strong enough for contact incubation.
3. Result of F.S. in oviraptorosaurian clutches suggests
that they would not break their eggs in the incubation
process with the center devoid of eggs .
4. The result from troodontid clutches shows the capacity
of bearing the body mass of parents, supporting the
hypothesis of contact-incubation in troodontids.
Factor of Safety (F.S.) A
B
C
Troodontidae and Oviraptoridae adopted different incubation strategies (Fig. 8A & B). In the
models of Oviraptoridae, we revised the load as the component force of body mass which is
calculated from the area ratio of egg and covering range (Figure 6 & 7B). From the result (Fig.
8C), the egg of Troodon formosus is within the normal range of extant avian,
which supports Troodon formosus could contact incubate. The F.S. of Oviraptoridae are
higher than the critical boundary as expected.